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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On the identifiability of binary Segre products


Authors: Cristiano Bocci and Luca Chiantini
Journal: J. Algebraic Geom. 22 (2013), 1-11
DOI: https://doi.org/10.1090/S1056-3911-2011-00592-4
Published electronically: November 22, 2011
MathSciNet review: 2993044
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Abstract | References | Additional Information

Abstract: We prove that a product of $ m>5$ copies of $ \mathbb{P}^1$, embedded in the projective space $ \mathbb{P}^r$ by the standard Segre embedding, is $ k$-identifiable (i.e. a general point of the secant variety $ S^k(X)$ is contained in only one $ (k+1)$-secant $ k$-space), for all $ k$ such that $ k+1\leq 2^{m-1}/m$.


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Additional Information

Cristiano Bocci
Affiliation: Universitá degli Studi di Siena, Dipartimento di Scienze Matematiche e Informatiche, Pian dei Mantellini, 44, I – 53100 Siena, Italy
Email: cristiano.bocci@unisi.it

Luca Chiantini
Affiliation: Universitá degli Studi di Siena, Dipartimento di Scienze Matematiche e Informatiche, Pian dei Mantellini, 44, I – 53100 Siena, Italy
Email: chiantini@unisi.it

DOI: https://doi.org/10.1090/S1056-3911-2011-00592-4
Received by editor(s): December 30, 2009
Received by editor(s) in revised form: February 21, 2011, and March 9, 2011
Published electronically: November 22, 2011

American Mathematical Society